Nonlinear models of electronic components, such as transistors, for circuit simulation are important tools for design of nonlinear integrated circuits, monolithic microwave integrated circuits (MMICs), and the like. The nonlinear electronic component models represent performance characteristics of underlying device technology in mathematical form, which may be used together with other components in a circuit simulator to develop and optimize design. The trend towards increasing energy efficiency, e.g., to extend battery life of mobile wireless communication devices, requires transistors, in particular, to operate under conditions that are becoming more nonlinear. Also, the wider bandwidths of modern signal formats, such as long term evolution (LTE), WiMAX and wideband code division multiple access (WCDMA), are stimulating the transistors with complex modulation formats, including more complicated signals with higher peak-to-average ratios. Further, transistors fabricated in new semiconductor materials, such as gallium nitride (GaN), and other compound semiconductor materials, such as gallium arsenide (GaAs), may exhibit complicated nonlinear dynamical effects in response to the complex modulation signals. Consequently, powerful and sophisticated nonlinear simulation models are needed to accurately and robustly incorporate these various effects that impact performance characteristics of the nonlinear integrated circuits.
Conventional nonlinear electronic component models, which may be referred to as “compact” models, are generally implemented in circuit simulators as nonlinear, ordinary differential equations, or equivalently, nonlinear equivalent circuit elements arranged in a specific equivalent circuit topology. For a specific equivalent circuit topology, the nonlinear constitutive relations are typically fixed, closed-form expressions defining terminal currents as nonlinear functions of controlling variables, such as voltages.
Conventional data used in these models are typically obtained from a variety of disparate and often limited measurements. Conventional data include DC IV characteristics and linear S-parameters versus bias and frequency, sometimes obtained over a range of ambient temperatures. These types of conventional data generally are not sufficient to separate all dynamical effects from one another, such as dynamic self-heating and trapping phenomena. More recently, pulsed-bias measurements, and pulsed S-parameter data have been used to help gain insight into device performance and, to some degree, separate dynamical effects from one another. However, the timescales of the pulsed-bias measurements are typically limited to a range of 0.1 μs to 1.0 μs, which is much slower than the characteristic timescales of a radio frequency (RF) input signal, which may be in a range of 0.01 ns to 1.0 ns.
In addition, the available model nonlinear constitutive relations are not sufficiently complex or accurate. They generally do not take into account the detailed dependence on the multiple dynamical variables. The choice of functional form for the constitutive relations may be based on physics, for example, but the resulting expressions may be too simple to fit the detailed measured performance characteristics of the actual nonlinear electronic components. An alternative is to postulate empirical nonlinear constitutive relations with unknown coefficients, which are then “extracted” by an optimization procedure to fit the functions to appropriate data. For semiconductor devices, such as GaN and GaAs transistors, that exhibit complicated dynamical behavior, including self-heating and trap capture and emission, the detailed functional dependence on all the relevant dynamical variables (e.g., instantaneous terminal voltages, junction temperature, trap states associated with gate-lag and drain lag, etc.) associated with these effects is quite complicated. Specific simplifying assumptions about the coupling of the relevant dynamical variables are inevitably invoked to obtain a sufficiently simple set of nonlinear constitutive relations to define, for example, the current as a function of all the relevant variables. Such simplifying assumptions lead to a loss of generality and a significant loss of accuracy for the resulting model. Therefore, no matter what parameter values are extracted, the accuracy of the model may be limited due to the over-simplified a priori form of the underlying constitutive relations.
Recently, more advanced types of nonlinear stimulus-response data, called waveform data, are beginning to become available with the introduction of waveform measurement systems such as Nonlinear Vector Network Analyzers (NVNAs) and Large-Signal Network Analyzers (LSNAs). However, the same overly simple a priori constitutive relations are typically used as optimization targets in the extraction procedure. In other words, there is no general, procedural approach to constructing the nonlinear constitutive relations for complicated dynamical models directly from the device data, conventional or modern waveform data.